Much effort has been directed in the past to making the trajectory of projectiles deviate predictably from their expected flight path, and to magnify such deviation. The ability to do this is highly prized, for example, by baseball pitchers, who strive to improve their curve balls. The manufacturers of toys and games have also sought to develop new and different game balls, and launch-assist equipment, so that when the ball is launched either from the hand or from launch-assist equipment, unusually curved flight paths occur.
As general background for this invention, it is accepted that a spherical projectile, such as a ball, will traverse a generally parabolic path, as viewed in the vertical plane, when launched into ballistic flight in still air. When similarly launched in still air rotating about a vertical or near vertical axis, the trajectory of the ball will also curve in a horizontal plane.
This horizontal curvature resulting when a ball rotates (spins) in ballistic flight results from a special case of the Bernoulli Principle known as the Magnus effect. As the ball spins in flight, points on one horizontal side travel in the same direction as the center of mass, and points on the opposite side travel in the opposite direction. The front and rear horizontal surfaces of the ball are also travelling in directions opposite to each other. The rotation of the ball in the air creates a net force perpendicular to the flight path so that the direction of horizontal curvature in flight is in the same direction as the travel of the front of the spinning ball. This horizontal deviation of the flight path of the spinning ball is hereinafter referred to as the Magnus curve of the ball.
Other aspects of the background leading to the present invention relate to Boundary Layer, Laminar Sublayer, Aerodynamic Roughness, Separation, Wake, Drag, Lift, Reynolds number and Critical Reynolds number. When an aerodynamically smooth body travels through a viscous fluid, there is a zone between the body and the free stream of the fluid called the boundary layer. Flow in the boundary layer near the leading part of the body is laminar but as the layer extends along the surface of the body backwards from the leading portion, a transition line is reached, if the surface is long enough, at which the flow in the boundary layer becomes turbulent. Whether or not flow in the boundary layer is turbulent there still exists deep to the boundary layer and adjacent to the surface of the body a narrow region of fluid in which the flow remains laminar; this is known as the laminar sublayer. Aerodynamic smoothness implies that no parts of the surface of the body protrude through the laminar sublayer. When parts of the surface of the body do protrude through the laminar sublayer, the surface is said to be aerodynamically rough. Roughness may be present to a greater or lesser degree and is quantifiable.
As the boundary layer extends backwards from the leading portion of the body it becomes progressively thicker and the velocity profile within the boundary layer changes, the velocity in the layers closer to the surface of the body decreasing progressively. At the level where the velocity in the deeper layer first falls to zero the boundary layer separates from the body and the zone to the rear of this level is called the wake. The wake retards forward motion. All forces retarding forward motion are called drag and the larger the area of surface from which the wake arises the greater is this form of drag. The boundary layer itself is associated with a form of drag called viscous drag.
When forward flight energy is translated into deviations from expected trajectory, these deviations may be regarded as lift (independently of the actual direction of such deviation) and such translation is associated with another form of drag called induced drag.
If the outer laminar boundary layer is made turbulent, then the boundary layer will not separate until further back from the leading part of the body, with the result that the wake is narrower and this source of drage is diminished. Although the viscous drag of the turbulent boundary layer is higher than that of the laminar boundary layer, the total drag is less because the wake is so much narrower. Aerodynamic roughness can cause such turbulence and thereby result in diminution in total drag. This phenomenon has been utilized in the design of golf balls which are manufactured with patterns of depressions (or elevations, according to one's perspective) on the surface. When struck by a golf club in the usual way, the surface pattern is believed to increase the Magnus effect of the spinning ball, increasing lift, narrowing the wake and more than counterbalancing any increase in viscous drag so that the now aerodynamically roughened golf ball will travel further than an aerodynamically smooth golf ball.
The transition from laminar to turbulent flow is promoted: (1) by increasing the relative velocity, u, of surface and free fluid stream; (2) by decreasing kinematic viscosity, v of the fluid, here air, and (3) at increasing distance, x, from the leading portion of the body. These three variables are combined to form a characteristic number called the Reynolds number, so that, EQU R=u.x/v
For the purposes of this invention, relative velocity, u, is the control variable.
The relation between drag and R for a given sphere is shown in FIG. 1 of the drawings. Generally, as the velocity increases, R increases and drag increases; conversely as velocity decreases, R decreases and drag decreases. The transition from laminar to turbulent flow occurs over a critical range of Reynolds number. Above that critical range flow will be turbulent and below that range it will be laminar. As points on the surface of the body pass through the critical range of Reynolds number, flow will tend to change from laminar to turbulent or from turbulent to laminar, according to whether the points are accelerating or decelerating. At the critical range of Reynolds number, the general trend is interrupted and, over a short span of R values, as velocity increases, and therefore R values increase, drag decreases. Conversely, as velocity decreases, and therefore R values decrease, drag increases. In ballistic spinning flight the speed of both the center of mass and of spin are decreasing so that drag is generally decreasing except during passage through the critical range of R values, when drag transiently increases. With a smooth ball the critical range of R values is much higher than with a rough ball and to pass through the critical range requires a combination of ballistic speed and spin not readily attainable by the human hand, although readily attainable with launch assisting equipment. Furthermore, since the lateral forces involved are so small, the greater momentum and higher speeds will minimize the amount of deviation. Appropriate roughening of the surface of the ball will lower the critical range of R values so that to pass through the critical range requires a lower range of ballistic speeds and spin, readily obtainable by the human hand. The lower momentum and lower speeds will permit greater deviations from expected flight trajectory.
If the free air-stream velocity and speed of rotation are high enough, then the critical range of Reynolds number could be exceeded at surface points on both sides of the sphere. As the free air-stream velocity and speed of rotation decrease in ballistic flight, points first on one side and then on the other side would fall through the critical range of Reynolds number and total drag would increase first on one side and then on the other. This would create asymmetric lateral forces whose algebraic sum opposed the Magnus curve and if of sufficient magnitude would cause the ball to curve in the opposite (anti-Magnus) direction until both sides had passed through the critical range of Reynolds number, when the Magnus curve would resume. Thus the ball would be directed along a flight path having a triple curve representing successively a Magnus curve, an anti-Magnus curve and finally a Magnus curve again.
According to the conditions at the beginning of ballistic flight (launch) and at the end of ballistic flight (where the ball strikes a bat, ground or hand, for example) the flight path could also shown one of two double curves (Magnus followed by anti-Magnus or anti-Magnus followed by Magnus) or one of two single curves, Magnus or anti-Magnus. If the design of the roughness and the axis of spin were appropriately adjusted unusual deviations in planes other than the horizontal, e.g., the vertical plane, could be achieved. The anti-Magnus curve singly and in various combinations with the Magnus curve are novel features of the present invention.